Characteristics of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens downwards or upwards.

Front

How can you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What are the possible number of solutions for a quadratic equation?

Back

A quadratic equation can have two solutions, one solution, or no real solutions, depending on the discriminant (b² - 4ac).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac that determines the nature of the roots of the quadratic equation.

Front

What is a maximum value in a quadratic function?

Back

The maximum value is the highest point of the parabola, occurring at the vertex when the parabola opens downwards.

Front

What is a minimum value in a quadratic function?

Back

The minimum value is the lowest point of the parabola, occurring at the vertex when the parabola opens upwards.